Boundary properties of arbitrary functions
Izvestiya. Mathematics, Tome 1 (1967) no. 1, pp. 1-12 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the dependence between various sets of limiting boundary values of an arbitrary function $f$ of $z$. In particular we show that the Plesner theorem on angular boundary values of analytic functions generalizes in a natural way to arbitrary functions.
@article{IM2_1967_1_1_a0,
     author = {E. P. Dolzhenko},
     title = {Boundary properties of arbitrary functions},
     journal = {Izvestiya. Mathematics},
     pages = {1--12},
     year = {1967},
     volume = {1},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_1_a0/}
}
TY  - JOUR
AU  - E. P. Dolzhenko
TI  - Boundary properties of arbitrary functions
JO  - Izvestiya. Mathematics
PY  - 1967
SP  - 1
EP  - 12
VL  - 1
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1967_1_1_a0/
LA  - en
ID  - IM2_1967_1_1_a0
ER  - 
%0 Journal Article
%A E. P. Dolzhenko
%T Boundary properties of arbitrary functions
%J Izvestiya. Mathematics
%D 1967
%P 1-12
%V 1
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1967_1_1_a0/
%G en
%F IM2_1967_1_1_a0
E. P. Dolzhenko. Boundary properties of arbitrary functions. Izvestiya. Mathematics, Tome 1 (1967) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/IM2_1967_1_1_a0/

[1] Fatou P., “Séries trigonometriques et séries de Taylor”, Acta Math., 30 (1906), 335–400 | DOI | MR | Zbl

[2] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M., 1950

[3] Collingwood E. F., “Sur le comportement à la frontière d'une fonction meromorphe dans le circle unitè”, Compt. rend. Acad. Sci., 240 (1955), 1502–1504 | MR | Zbl

[4] Dolzhenko E. P., “O granichnykh teoremakh edinstvennosti i o povedenii analiticheskikh funktsii vblizi granitsy”, Dokl. AN SSSR, 129:1 (1959), 23–26 | Zbl

[5] Collingwood E. F., “Cluster sets of arbitrary functions”, Froc. Nat. Acad. Sci. USA, 46:9 (1960), 1236–1242 | DOI | MR | Zbl

[6] Erdös P., Piranian G., “Restricted cluster sets”, Math. Nachr., 22 (1960), 155–158 | DOI | MR | Zbl

[7] Saks S., Teoriya integrala, IL, M., 1949

[8] Dolzhenko E. P., Granichnye svoistva analiticheskikh i garmonicheskikh funktsii, Dissertatsiya, MGU, M., 1964